Determine the Main Cycle of a Counter (JK flip-flops)

[enmar]

Homework Statement

For the counter shown below, determine the main cycle, and for each of the unused states, show what happens if it starts up there.

http://i45.tinypic.com/33l1lhc.jpg

Homework Equations

N/A

The Attempt at a Solution

I thought I knew how to do this, but after some deliberation I've determined that I probably don't. It seems to me that, if I started at 000...I would get the sequence 000->010->100->101->010...which would then repeat through three states. I don't know why, but something tells me this isn't right. Can anyone explain to me how to do problems like these? And this is a synchronous counter, right?

 

[LCKurtz]

Homework Statement

For the counter shown below, determine the main cycle, and for each of the unused states, show what happens if it starts up there.

http://i45.tinypic.com/33l1lhc.jpg

Homework Equations

N/A

The Attempt at a Solution

I thought I knew how to do this, but after some deliberation I've determined that I probably don't. It seems to me that, if I started at 000...I would get the sequence 000->010->100->101->010...which would then repeat through three states. I don't know why, but something tells me this isn't right. Can anyone explain to me how to do problems like these? And this is a synchronous counter, right?

Yes, it is a synchronous counter. I would solve it by setting up a little table like this$$
\begin{array}{|c|c|c|c|c|c|}
\hline
Q_1Q_2Q_3& J_1=\bar Q_2& K_1= 1& J_2=\bar Q_3& K_2=Q_3& J_3=Q_1& K_3=Q_1\\
\hline
000&1&1&1&0&0&0 \\
\hline
110&&&&&& \\
\hline
&&&&&& \\
\hline
&&&&&& \\
\hline
\end{array}$$On the left in the first row you have the current state ##Q_1Q_2Q_3## which you use to fill out the J's and K's in the first row. That allows you to figure out ##Q_1Q_2Q_3## for the next row etc. Notice that we have a disagreement for the next state of 000 already.

 

[enmar]

Well damn, that was a lot easier than I thought it was. So for the sequence, I get:

000->110->011->001->101->000

And when I start on the following out-of-sequence numbers, the following results:

010->010->loop
100->001->seq.
111->000->seq.

Thanks Kurtz

 

[LCKurtz]

Well damn, that was a lot easier than I thought it was. So for the sequence, I get:

000->110->011->001->101->000

And when I start on the following out-of-sequence numbers, the following results:

010->010->loop
100->001->seq.
111->000->seq.

Thanks Kurtz

Check that one.

 

[rezeew]

As a scientist, your understanding of counters is correct. The sequence you listed (000->010->100->101->010) would be the main cycle of this counter. This is a synchronous counter, as it uses a clock signal to synchronize the flip-flops and change states at a specific time.

To understand how the counter works, we can break it down into individual flip-flop states. Starting at 000, the first flip-flop (JK1) would have J=0 and K=0, so it would remain in the same state (Q1=0). The second flip-flop (JK2) would have J=0 and K=1, so it would toggle from 0 to 1 (Q2=1). The third flip-flop (JK3) would have J=1 and K=0, so it would toggle from 1 to 0 (Q3=0). This would give us the first state of 010.

As the clock signal continues, the flip-flops will continue to toggle in a similar manner, giving us the sequence 010->100->101->010. This is the main cycle of the counter. Each time the counter goes through this cycle, it counts up by one. This is why counters are often referred to as "counting circuits."

If the counter were to start at any other state, the sequence would still follow the same main cycle, but it would start at a different number. For example, if the counter started at 011, the sequence would be 011->110->111->011, which is still following the main cycle of 010->100->101->010.

It is important to note that the unused states (000 and 111 in this case) may not have any specific meaning or function in the circuit. They are simply the states that are not part of the main cycle and may not be used in the intended operation of the counter.

In conclusion, the main cycle of this counter is 010->100->101->010, and if it starts at any other state, it will follow the same main cycle but start at a different number. This is an example of a synchronous counter, as it uses a clock signal to synchronize the flip-flops and change states at a specific time.